2x^2-38x=7x^2-3x-24

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Solution for 2x^2-38x=7x^2-3x-24 equation:


Simplifying
2x2 + -38x = 7x2 + -3x + -24

Reorder the terms:
-38x + 2x2 = 7x2 + -3x + -24

Reorder the terms:
-38x + 2x2 = -24 + -3x + 7x2

Solving
-38x + 2x2 = -24 + -3x + 7x2

Solving for variable 'x'.

Reorder the terms:
24 + -38x + 3x + 2x2 + -7x2 = -24 + -3x + 7x2 + 24 + 3x + -7x2

Combine like terms: -38x + 3x = -35x
24 + -35x + 2x2 + -7x2 = -24 + -3x + 7x2 + 24 + 3x + -7x2

Combine like terms: 2x2 + -7x2 = -5x2
24 + -35x + -5x2 = -24 + -3x + 7x2 + 24 + 3x + -7x2

Reorder the terms:
24 + -35x + -5x2 = -24 + 24 + -3x + 3x + 7x2 + -7x2

Combine like terms: -24 + 24 = 0
24 + -35x + -5x2 = 0 + -3x + 3x + 7x2 + -7x2
24 + -35x + -5x2 = -3x + 3x + 7x2 + -7x2

Combine like terms: -3x + 3x = 0
24 + -35x + -5x2 = 0 + 7x2 + -7x2
24 + -35x + -5x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
24 + -35x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-4.8 + 7x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + 7x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + 7x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + 7x + x2 = 0 + 4.8
7x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
7x + x2 = 4.8

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 4.8 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 4.8 + 12.25

Combine like terms: 4.8 + 12.25 = 17.05
12.25 + 7x + x2 = 17.05

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 17.05

Calculate the square root of the right side: 4.129164564

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.129164564 and -4.129164564.

Subproblem 1

x + 3.5 = 4.129164564 Simplifying x + 3.5 = 4.129164564 Reorder the terms: 3.5 + x = 4.129164564 Solving 3.5 + x = 4.129164564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.129164564 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.129164564 + -3.5 x = 4.129164564 + -3.5 Combine like terms: 4.129164564 + -3.5 = 0.629164564 x = 0.629164564 Simplifying x = 0.629164564

Subproblem 2

x + 3.5 = -4.129164564 Simplifying x + 3.5 = -4.129164564 Reorder the terms: 3.5 + x = -4.129164564 Solving 3.5 + x = -4.129164564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.129164564 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.129164564 + -3.5 x = -4.129164564 + -3.5 Combine like terms: -4.129164564 + -3.5 = -7.629164564 x = -7.629164564 Simplifying x = -7.629164564

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.629164564, -7.629164564}

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